Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19149726 | C2 | semidirect |
| 2. #26012291 | C2 | semidirect |
| 3. #26012289 | C2 | semidirect |
| 4. #26012067 | C2 | semidirect |
| 5. #26011675 | C2 | semidirect |
| 6. #26011665 | C2 | semidirect |
| 7. #26011509 | C2 | semidirect |
| 8. C2×#19149597 | C2 | semidirect |
| 9. #421×C173 | C2 | semidirect |
| 23. #19149712 | C22 | semidirect |
| 25. #19149709 | C22 | semidirect |
| 27. #19149707 | C22 | semidirect |
| 29. #19149704 | C22 | semidirect |
| 33. #19149679 | C22 | semidirect |
| 34. #19149667 | C22 | semidirect |
| 37. #19149607 | C22 | semidirect |
| 38. #19149597 | C22 | semidirect |
| 42. #104×C173 | C22 | semidirect |
| 185. C173 | #3020 | semidirect |
| 194. #421 | D173 | semidirect |
| 227. #104 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| #26012291 | 2 |
| #26012289 | 2 |
| #26012067 | 2 |
| #26011675 | 2 |
| #26011665 | 2 |
| #26011509 | 2 |
| C2×#19149597 | 2 |
| #421×C173 | 2 |
| #3020 | 173 |